CHEM. 542 Spring 2010
Taught by Dana D. Dlott and Nancy Makri
Course Outline
1.
Fundamentals of time-dependent quantum mechanics (NM ~4 lectures)
The time-dependent Schrdinger equation. Time-independe
Chem. 542
Assignment by Nancy Makri
PROBLEM 9
Convert the Bloch equations for a TLS coupled to a harmonic dissipative bath to the site
(left/right) representation.
Chem. 542
Assignment by Nancy Makri
PROBLEM 8
(a) Calculate the equilibrium values of the TLS populations at a given temperature.
(b) Use the Redfield equations for a TLS coupled to a dissipative harm
Chem. 542
Assignment by Nancy Makri
PROBLEM 7
Consider a two-state system, for which the eigenstates of the Hamiltonian are
1 =
where L , R
operator
1
( L + R ),
2
2 =
1
(LR
2
)
are orthonormal left-
Chem. 542
Assignment by Nancy Makri
PROBLEM 6
Consider a hydrogen atom, initially in its ground state. At t = 0 an electric field is turned
on in the z direction, whose strength changes linearly with
Chem. 542
Assignment by Nancy Makri
PROBLEM 5
Consider a harmonic oscillator of frequency in its ground state. At t = 0 a time
independent perturbation H1 (t ) = x is turned on. Using first order time
Chem. 542
Assignment by Nancy Makri
PROBLEM 4
In class we calculated the propagator for a free particle of mass m moving in one dimension.
a)
Using the one-dimensional result, find the propagator for
Chem. 542
Assignment by Nancy Makri
PROBLEM 3
(a)
For a time-independent Hamiltonian H , show that energy is conserved during time evolution.
(Hint: write the expectation value of the Hamiltonian at a
Chem. 542
Assignment by Nancy Makri
PROBLEM 2
In class we proved that time evolution preserves the norm of the wavefunction. Using again
the unitarity of the time evolution operator, show that wavefun
Chem. 542
Assignment by Nancy Makri
PROBLEM 1
The survival amplitude for a system initially described by the state (0) is defined as
C (t ) = (t ) (0)
i.e., C (t ) is a measure of the overlap of the p
CHEM. 542 Spring 2010
Required Textbook: Schatz and Ratner: Quantum Mechanics in Chemistry
Suggested Textbook: Feynmans Lectures in Physics, vol. 3
On reserve in the Chemistry Library:
Feynman lecture